In industrial applications, a substantial number of problems of efficient allocations of resources can be translated into the mathematical resolution of one or more constrained optimization problems, that is problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within a constrained allowed set.
As a subset of optimization problems, quadratic or conic optimization problems comprise one of the most important areas of nonlinear programming. They are currently solved in practical applications preferentially using variations of so-called “interior point methods”i that are generally relevant for convex optimization problems. Numerous practical problems, including problems in financial portfolio optimization, portfolio hedging, planning and scheduling, economies of scale, and engineering design, and control are naturally expressed as quadratic optimization problems.
We describe a new and more effective method for solving optimization problems in general by actually explicitly solving the apparently intractable Karush-Kuhn Tucker (KKT) equations and inequalities associated with the mathematical formulation of the problems. The general method outlined in our drawings and below is illustrated in detail through the resolution of classical quadratic and conic optimization problems.